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2D CHARGE RELAXATION IN GRAPHENE: GENERALIZEDTELEGRAPH EQUATIONS AND PSEUDO-RELATIVISTIC

INVARIANCEGENNADY I. ZEBREV

Department Micro- and Nanoelectronics, National Research Nuclear University MEPHI, Moscow, Russia ,e-mail: gizebrev@mephi.ru

Graphene

Imaginary mass in the KG equation means formally occurrence of tachyonspropagating with superluminal velocity!

[1] S. Salahuddin, M. Lundstrom , Transport effects on signal propagationin quantum wires, IEEE Trans. ED -52, 1734, 2005.

[2] G.I. Zebrev, Graphene Field Effect Transistors: Diffusion -Drift Theory,a chapter in Physics and Applications of Graphene Theory, Ed. by S.Mikhailov, Intech, 2011

[3] G.I. Zebrev et al. Influence of interface traps and electron -hole puddleson quantum capacitance and conductivity in graphene field-effecttransistors arXiv: cond-mat 1011.5127

[4] A. Polyanin , Handbook of Linear PD Equations for Scientist andEngineers, Chapman&Hall CRC, 2002

[Zebrev, 5] Graphene nanoelectronics: Electrostatics and Kinetics SPIEProc.2008

RPA Screening with Gates

2

5 6

7

8

2

2 22

, ,1,

r rrS

u t u t v u t

t t

0( , ) i t i qxu x t u e

1/22 2

1,2 2

12 4Si

v q

Diffusion pole and 2D diffusion

Quasi-static analysis and I-V GFET model

Publications

Introduction

Greens Function for Damping and Propagating modes

Tachyonic waves in dissipative graphene media?

, , ,1r

j r j r r

K

t t t

t L e

Momentum and Charge Conservation

,

, 0rr

j rt

t t

Semi-classical Boltzmann equation consequences

20 0 0

12K S F

h L

e n e k v

Kinetic inductance in graphene

, , ,r r rt t e t

Graphene gated structure = graphene + gate(s)

Electric neutrality ( qd